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# Lect24 - Announcement Homework available on web site Nave...

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Announcement Homework available on web site Naïve Bayes and Decision Trees Relevant Talk tomorrow (Friday) Prof. Jeff Siskind Purdue Embodied Intelligence 3405 SC, 2PM 1

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Perceptron Decision Boundary Compare weighted sum of inputs to a threshold Without loss of generality set x 0 = -1 then w 0 is This defines a decision surface Which is the equation of a hyperplane n i i i x w 1 0 0 n i i i x w 0 0 x w n i i i x w 2
Perceptron Learning (Widrow-Hoff or delta rule) w x + Percep w + - percep w ( x ) assigns + or 1 if w x > 0 (vector dot product) else it assigns or 0 err = label( x ) percep w ( x ) 0: correct -1: false pos 1: false neg Here, false neg: w x < 0 but it should be > 0 loss = distance from boundary = - err w x Want to adjust w i ’s to reduce this loss Loss fcn gradient is direction of greatest increase in loss with w Want the opposite: step w in direction - w loss 3

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Perceptron Learning (Widrow-Hoff or delta rule) w x + Percep w + - Loss function = - err w x Want the opposite: step w in direction - w loss What is w loss? View - err w x as a function of w w (- err w x ) = - err x So - w (- err w x ) = err x Update w according to: w = err x where is a learning rate 4
Perceptron Learning (Widrow-Hoff or delta rule) w x + Percep w + - Choose a learning rate Compute w = err x Add w to w w 5

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w x + Percep w + - Choose a learning rate ; initialize w arbitrarily (small works best) Compute w = err x Add w to w Repeatedly cycle through training examples Learn (always and only) on errors w New perceptron rotates to reduce error If x were a false positive… Perceptron Learning (Widrow-Hoff or delta rule) 6
If the points are linearly separable, the algorithm a) will halt b) will find a separator (The celebrated Perceptron Convergence Theorem) Choosing wisely will speed convergence If the points are not linearly separable, the algorithm may not halt.

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